Atomistic Description

A Graph Convolutional Network, or GCN, is an approach for semi-supervised learning on graph-structured data. It is based on an efficient variant of convolutional neural networks which operate directly on graphs. The choice of convolutional architecture is motivated via a localized first-order approximation of spectral graph convolutions. The model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes.

A Graph Attention Network (GAT) is a neural network architecture that operates on graph-structured data, leveraging masked self-attentional layers to address the shortcomings of prior methods based on graph convolutions or their approximations. By stacking layers in which nodes are able to attend over their neighborhoods’ features, a GAT enables (implicitly) specifying different weights to different nodes in a neighborhood, without requiring any kind of costly matrix operation (such as inversion) or depending on knowing the graph structure upfront. See here for an explanation by DGL.

There are at least eight notable examples of models from the literature that can be described using the Message Passing Neural Networks (MPNN) framework. For simplicity we describe MPNNs which operate on undirected graphs $G$ with node features $x_{v}$ and edge features $e_{vw}$. It is trivial to extend the formalism to directed multigraphs. The forward pass has two phases, a message passing phase and a readout phase. The message passing phase runs for $T$ time steps and is defined in terms of message functions $M_{t}$ and vertex update functions $U_{t}$. During the message passing phase, hidden states $h_{v}^{t}$ at each node in the graph are updated based on messages $m_{v}^{t+1}$ according to $$ m_{v}^{t+1} = \sum_{w \in N(v)} M_{t}(h_{v}^{t}, h_{w}^{t}, e_{vw}) $$ $$ h_{v}^{t+1} = U_{t}(h_{v}^{t}, m_{v}^{t+1}) $$ where in the sum, $N(v)$ denotes the neighbors of $v$ in graph $G$. The readout phase computes a feature vector for the whole graph using some readout function $R$ according to $$ \hat{y} = R(\\{ h_{v}^{T} | v \in G \\}) $$ The message functions $M_{t}$, vertex update functions $U_{t}$, and readout function $R$ are all learned differentiable functions. $R$ operates on the set of node states and must be invariant to permutations of the node states in order for the MPNN to be invariant to graph isomorphism.

Per the authors, Graph Isomorphism Network (GIN) generalizes the WL test and hence achieves maximum discriminative power among GNNs.

SchNet is an end-to-end deep neural network architecture based on continuous-filter convolutions. It follows the deep tensor neural network framework, i.e. atom-wise representations are constructed by starting from embedding vectors that characterize the atom type before introducing the configuration of the system by a series of interaction blocks.

Shifted Softplus is an activation function ${\rm ssp}(x) = \ln( 0.5 e^{x} + 0.5 )$, which SchNet employs as non-linearity throughout the network in order to obtain a smooth potential energy surface. The shifting ensures that ${\rm ssp}(0) = 0$ and improves the convergence of the network. This activation function shows similarity to ELUs, while having infinite order of continuity.

Galactica is a language model which uses a Transformer architecture in a decoder-only setup with the following modifications: - It uses GeLU activations on all model sizes - It uses a 2048 length context window for all model sizes - It does not use biases in any of the dense kernels or layer norms - It uses learned positional embeddings for the model - A vocabulary of 50k tokens was constructed using BPE. The vocabulary was generated from a randomly selected 2% subset of the training data

The GATv2 operator from the “How Attentive are Graph Attention Networks?” paper, which fixes the static attention problem of the standard GAT layer: since the linear layers in the standard GAT are applied right after each other, the ranking of attended nodes is unconditioned on the query node. In contrast, in GATv2, every node can attend to any other node. GATv2 scoring function: $e_{i,j} =\mathbf{a}^{\top}\mathrm{LeakyReLU}\left(\mathbf{W}[\mathbf{h}_i \, \Vert \,\mathbf{h}_j]\right)$

Principal Neighbourhood Aggregation (PNA) is a general and flexible architecture for graphs combining multiple aggregators with degree-scalers (which generalize the sum aggregator).

As they carry great potential for modeling complex interactions, graph neural network (GNN)-based methods have been widely used to predict quantum mechanical properties of molecules. Most of the existing methods treat molecules as molecular graphs in which atoms are modeled as nodes. They characterize each atom's chemical environment by modeling its pairwise interactions with other atoms in the molecule. Although these methods achieve a great success, limited amount of works explicitly take many-body interactions, i.e., interactions between three and more atoms, into consideration. In this paper, we introduce a novel graph representation of molecules, heterogeneous molecular graph (HMG) in which nodes and edges are of various types, to model many-body interactions. HMGs have the potential to carry complex geometric information. To leverage the rich information stored in HMGs for chemical prediction problems, we build heterogeneous molecular graph neural networks (HMGNN) on the basis of a neural message passing scheme. HMGNN incorporates global molecule representations and an attention mechanism into the prediction process. The predictions of HMGNN are invariant to translation and rotation of atom coordinates, and permutation of atom indices. Our model achieves state-of-the-art performance in 9 out of 12 tasks on the QM9 dataset.

The Multiplex Molecular Graph Neural Network (MXMNet) is an approach for the representation learning of molecules. The molecular interactions are divided into two categories: local and global. Then a two-layer multiplex graph $G = \\{ G_{l}, G_{g} \\}$ is constructed for a molecule. In $G$, the local layer $G_{l}$ only contains the local connections that mainly capture covalent interactions, and the global layer $G_{g}$ contains the global connections that cover non-covalent interactions. MXMNet uses the Multiplex Molecular (MXM) module that contains a novel angle-aware message passing operated on $G_{l}$ and an efficient message passing operated on $G_{g}$.